data from the book introduction to biomechanical ... · author: shigehiro hashimoto kogakuin...
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Author: Shigehiro Hashimoto
Kogakuin University,
Department of Mechanical Engineering,
Biomedical Engineering
Data from the book "Introduction
to Biomechanical Engineering (in
Japanese)“: published by Corona
Publishing Co., Ltd. Tokyo, Japan.
© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan
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Fig. 3.1: Spring
Dilation Dilation Dilation
Dilation
Weight
© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan
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Fig. 3.2: Mode of deformation
Extension
Compression
Bending
Twist
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Fig. 3.3: Orientation of cells and
matrices
Orientation of extracellular matrices
Orientation of cells
Longitudinal direction of extracellular matrix
Longitudinal direction of cell
(Endothelium)
© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan
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Fig. 3.4: Direction of forces at tube
wall
Radial
Tangential
Longitudinal
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Fig. 3.5: Transmission of force
(A)
(B)
?
Cell Force
Cell
Flow
Shear field
Scaffold
Wall
Slip at attachment part
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Fig. 3.6: Fixation
Fixation
Measurement
Mark
Mark
Friction
Pressure
Pressure
Tension
Tension(a) (c)(b)
Compliance
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Fig. 3.7: Origin
Deformation
Force
Origin?
Linear part
composite
material
© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan
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Normal stress
Fig. 3.8: Stress
Shear stress
Surface Surface
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Fig. 3.9: Poisson’s ratio
Deformation
x+Δxx
y y-Δy
Force
Force
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Tension
Fig. 3.10: Strains in tension
Compressive strainShear strain
Tensile strain
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Fig. 3.11: Strain gauge
Tension
Wire
thick &
short
Wire
small &
long
Resistance change
StrainStrain gaugeStrain gauge
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Fig. 3.12: Stress-strain diagram
Strain ε
Stress τYield point
Elastic
Elastic modulus E
Plastic
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Fig. 3.13: True stress
Deformation
x1x0
y0 y1
A0 A1
F1
F1
F0
F0
τ0=F0 / A0 τ1=F1 / A1: True stress
τ=F1 / A0: Nominal stress
© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan
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ΔP
r
γ
r
ΔPπr2=2πr γ (3.10)
ΔP=2γ/r (3.11)
Equation of Young-Laplace
Fig. 3.14: Balance of forces in
hemisphere
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Fig. 3.15: Tensile force at membrane of
erythrocyte
P1
P2
P3
r1r2
γ
Capillary
Erythrocyte
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Fig. 3.16: Bending
F
F/ 2
x
Bending moment
Shearing force
Positive
PositiveM=xF/ 2
x
F/ 2
F/ 2
F/ 2
a/ 2 a/ 2
(a)
(b)
F/2+F/2-F =0 (3.12)
-(a/2)F+a(F/2)=0 (3.13)
© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan
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Fig. 3.17: Simple & rigid support
F
F/ 2
x
F/ 2a/ 2 a/ 2
F
F
x
a
Rigid support
Simple support
M
(a) Simple support
(b) One side rigid support
Simple support
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Fig. 3.18 Three-point bending test
F1
F1/ 2 F1/ 2
Shearing force diagram
Bending moment diagram
F
F1/ 2
F1/ 2
a
F1a/ 4
a/ 2
0 x
M
x
a
a
a/ 2
a/ 2
0
x(a)
(b)
(c)
© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan
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Fig. 3.19: Four-point bending test
F1 F1
F1 F1
Shearing force diagram
Bending moment diagram
a
a/ 3
F1
F1
F1a/ 3
xa
x
a
x
F
M
0
0
a/ 3
2a/ 3a/ 3
2a/ 3
(a)
(b)
(c)
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Fig. 3.20: Center line and strain
Center line
y x
Cross-sectional area:
A
dA y
z
Cross
section
Iz=∫y2 dA (3.15)
Moment of inertia: Iz
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Fig. 3.21: Yield and fracture
Strain
Stress
Yield point
Maximum strain
Strength Fracture
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Fig. 3.22: Repetitive load
Stress
(b) Compression
(c) Extension & Compression
Time
Stress
(a) Extension
Time
TimeStress
0
0
0
Amplitude
Period
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Fig. 3.23 Fracture surface
Fracture
surface
DimpleStriation
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Fig. 3.24: Stress amplitude vs.
number of cycles
Destructive
area
Non-
destructive
area
Destruction
Non-
destruction
Number of cycles
Stress
amplitude
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Fig. 3.25: Erythrocyte fatigue in flow
Shear
stress
(Shear rate)×(Exposure time)
Hemolysis ratio <0.01
Hemolysis ratio>0.01
Tensile
Compression
Tensile
Compression
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Fig. 3.26: Erythrocyte destruction
0.01 mm
Hemolysis
Periodical
deformation
(Ellipsoid)
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Fig. 3.27: Close-packed lattice
Close-packed
hexagonal
lattice
Face-
centered
cubic lattice
ABCABC ABABAB
A
B
C
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Fig. 3.28: Surface
Inside
Surface
Interaction
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Fig. 3.29: Poly-crystal
Crystal grain
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Fig. 3.30: Lattice defect
DislocationVacancy
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Fig. 3.31: Stress concentration
Curvature
Notch
Stress
concentration
Force
Force
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Fig. 3.32(a): Orientation of
endothelial cells
0.1 mm
Flow
Orientation
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Fig. 3.32(b): Orientation of C2C12
0.1 mm
Flow
Orientation
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Fig. 3.33: Electrodes
10 mmCell culture
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Fig. 3.34: Force applied on laryngoscope
© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan
Tongue
Superior
incisor
Epiglottis
Laryngoscope
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Fig. 3.35: Phantom
(a) Copper sulfate
aqueous solution
(b) MRI (magnetic
resonance image)
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Fig. 3.36: Penetration of phenol-red
into agar
Agar
Phenol red
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Q. 3.3 Fig. 3.37: Face-centered
cubic unit lattice
r
r
r
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